Image Segmentation as an Optimization Problem

IT IS ACCEPTED THAT IMAGE SEGMENTATION IS A MAIN PROBLEM IN COMPUTER VISION. ITS GOOD SOLUTION DETERMINES THE WELL PERFORMANCE OF THE AUTOMATIC RECOGNITION SYSTEM IMPLIED. IN THIS PAPER WE PRESENT A NEW WAY TO SOLVE THIS PROBLEM. FOR THIS WE TREAT THE IMAGE SEGMENTATION PROBLEM AS AN OPTIMIZATION PROBLEM, AND JUSTIFY THE UTILITY OF THE VARIATIONAL APPROACH TO SOLVE IT. WE ALSO INTRODUCE A COMMON FRAMEWORK BASED ON MUMFORD-SHAH 'S APPROACH WHERE MOST IMAGE SEGMENTATION ALGORITHMS CAN BE EXPRESSED. F OR THIS WE USE THE THEORIES OF CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS AND SOME OF THE IDEAS OF TIKHONOV FOR THE SOLUTION OF ILL-POSED PROBLEMS. USING THIS NEW FRAMEWORK, WE SHOW HOW TO CREATE NEW REASONABLE, FAST AND STABLE NUMERICAL ALGORITHMS USEFUL TO SEGMENT COMPLICATED REAL IMAGES EVEN IF SOME INITIAL INFORMATION IS LOST. WE FINA[[Y TEST THE PERFORMANCE OF OUR DERIVED SEGMENTATION METHODS AND SOME VERY WE[[ KNOWN ONES. WE CONCLUDE THAT OUR METHODS ARE SUPERIOR IN THE SENSE THAT THEY ARE EVEN ABLE TO DETECT SMA[[ DETAILS THAT ARE NORMA[[Y LOST BY OTHERS AND THEY DO NOT DEPEND ON ANY THRESHOLD.